Rock friction and its implications for earthquake prediction examined via models of Parkfield earthquakes.

The friction of rocks in the laboratory is a function of time, velocity of sliding, and displacement. Although the processes responsible for these dependencies are unknown, constitutive equations have been developed that do a reasonable job of describing the laboratory behavior. These constitutive laws have been used to create a model of earthquakes at Parkfield, CA, by using boundary conditions appropriate for the section of the fault that slips in magnitude 6 earthquakes every 20-30 years. The behavior of this model prior to the earthquakes is investigated to determine whether or not the model earthquakes could be predicted in the real world by using realistic instruments and instrument locations. Premonitory slip does occur in the model, but it is relatively restricted in time and space and detecting it from the surface may be difficult. The magnitude of the strain rate at the earth's surface due to this accelerating slip seems lower than the detectability limit of instruments in the presence of earth noise. Although not specifically modeled, microseismicity related to the accelerating creep and to creep events in the model should be detectable. In fact the logarithm of the moment rate on the hypocentral cell of the fault due to slip increases linearly with minus the logarithm of the time to the earthquake. This could conceivably be used to determine when the earthquake was going to occur. An unresolved question is whether this pattern of accelerating slip could be recognized from the microseismicity, given the discrete nature of seismic events. Nevertheless, the model results suggest that the most likely solution to earthquake prediction is to look for a pattern of acceleration in microseismicity and thereby identify the microearthquakes as foreshocks.

Critical slip and time dependence in sea ice friction

Recent research into sea ice friction has focussed on ways to provide a model which maintains much of the clarity and simplicity of Amonton's law, yet also accounts for memory effects. One promising avenue of research has been to adapt the rate- and state- dependent models which are prevalent in rock friction. In such models it is assumed that there is some fixed critical slip displacement, which is effectively a measure of the displacement over which memory effects might be considered important. Here we show experimentally that a fixed critical slip displacement is not a valid assumption in ice friction, whereas a constant critical slip time appears to hold across a range of parameters and scales. As a simple rule of thumb, memory effects persist to a significant level for 10 s. We then discuss the implications of this finding for modelling sea ice friction and for our understanding of friction in general.

A unified friction description and its application to the simulation of frictional instability using the finite element method

This article first summarizes some available experimental results on the frictional behaviour of contact interfaces, and briefly recalls typical frictional experiments and relationships, which are applicable for rock mechanics, and then a unified description is obtained to describe the entire frictional behaviour. It is formulated based on the experimental results and applied with a stick and slip decomposition algorithm to describe the stick-slip instability phenomena, which can describe the effects observed in rock experiments without using the so-called state variable, thus avoiding related numerical difficulties. This has been implemented to our finite element code, which uses the node-to-point contact element strategy proposed by the authors to handle the frictional contact between multiple finite-deformation bodies with stick and finite frictional slip, and applied here to simulate the frictional behaviour of rocks to show its usefulness and efficiency.

Mechanism on Progressive Failure of a Faulted Rock Slope Due to Slip-Weakening

Slip-weakening is one of the characteristics of geological materials under certain loadings. Non-uniform rock structure may exist in the vicinity of the slip surface for a rock slope. Some portion of the slip surface may be penetrated but the other not. For the latter case, the crack or the fault surface will undergo shear deformation before it becomes a successive surface under a certain loading. As the slipped portion advances,slip-weakening occurs over a distance behind the crack tip. In the weakening zone, the shear strength will decrease from its peak value to residual friction level. The stress will redistribute along the surface of crack and in the weakening zone. Thus the changed local stress concentration leads the crack to extend and the ratio of penetration of the slip surface to increase. From the view of large-scale for the whole slip surface, the shear strength will decrease due to the damage of interior rock structure, and the faulted rock behaves as a softening material. Such a kind of mechanism performs in a large number of practical landslides in the zones experienced strong earthquakes. It should be noted that the mechanism mentioned above is different from that of the breakage of structural clay,in which the geological material is regarded as a medium containing structural lumps and structural bands. In this paper, the softening behavior of a faulted rock should be regarded as a comprehensive result of the whole complicated process including slip-weakening, redistribution of stress, extension of crack tip, and the penetration of the slip surface. This process is accompanied by progressive failure and abrupt structural damage. The size of slip-weakening zone is related to the undergoing strain. Once the relative slide is initiated (local or integrated), the effect of slip-weakening will behave in a certain length behind the crack tip until the formation of the whole slip surface.

A rate and state friction law for saline ice

Sea ice friction models are necessary to predict the nature of interactions between sea ice floes. These interactions are of interest on a range of scales, for example, to predict loads on engineering structures in icy waters or to understand the basin-scale motion of sea ice. Many models use Amonton's friction law due to its simplicity. More advanced models allow for hydrodynamic lubrication and refreezing of asperities; however, modeling these processes leads to greatly increased complexity. In this paper we propose, by analogy with rock physics, that a rate- and state-dependent friction law allows us to incorporate memory (and thus the effects of lubrication and bonding) into ice friction models without a great increase in complexity. We support this proposal with experimental data on both the laboratory (∼0.1 m) and ice tank (∼1 m) scale. These experiments show that the effects of static contact under normal load can be incorporated into a friction model. We find the parameters for a first-order rate and state model to be A = 0.310, B = 0.382, and μ0 = 0.872. Such a model then allows us to make predictions about the nature of memory effects in moving ice-ice contacts.

Permeability, overburden stress and friction coefficients of ODP Hole 190-1173A and 190-1174B

Permeability measured on three samples in a triaxial cell under effective confining pressure from 0.2 to 2.5 MPa ranges from 10**-18 to 10**-19 m**2. Overall, results indicate that permeability decreases with effective confining pressure up to 1.5 MPa; however, measurements at low effective pressure are too dispersed to yield a precise general relationship between permeability and pressure. When the effective pressure is increased from 1.5 to 2.5 MPa, permeability is roughly constant (~1-4 x 10**-19 m**2). Samples deformed in the triaxial cell developed slickenlined fractures, and permeability measurements were performed before and after failure. A permeability increase is observed when the sample fails under low effective confining pressure (0.2 MPa), but not under effective pressure corresponding to the overburden stress. Under isotropic stress conditions, permeability decrease related to fracture closure occurs at a relatively high effective pressure of ~1.5 MPa. Coefficients of friction on the fractures formed in the triaxial cell are ~0.4.

Measurements of velocity-dependent and slip-dependent frictional strength in laboratory friction experiments on natural samples from IODP Expedition 316 and ODP Hole 190-1174B

Slowslip forms part of the spectrum of fault behaviour between stable creep and destructive earthquakes. Slow slip occurs near the boundaries of large earthquake rupture zones and may sometimes trigger fast earthquakes. It is thought to occur in faults comprised of rocks that strengthen under fast slip rates, preventing rupture as a normal earthquake, or on faults that have elevated pore-fluid pressures. However, the processes that control slow rupture and the relationship between slow and normal earthquakes are enigmatic. Here we use laboratory experiments to simulate faulting in natural rock samples taken from shallow parts of the Nankai subduction zone, Japan, where very low-frequency earthquakes - a form of slow slip - have been observed.We find that the fault rocks exhibit decreasing strength over millimetre-scale slip distances rather than weakening due to increasing velocity. However, the sizes of the slip nucleation patches in our laboratory simulations are similar to those expected for the very lowfrequency earthquakes observed in Nankai. We therefore suggest that this type of fault-weakening behaviour may generate slow earthquakes. Owing to the similarity between the expected behaviour of slow earthquakes based on our data, and that of normal earthquakes during nucleation, we suggest that some types of slow slip may represent prematurely arrested earthquakes.

Micromechanical basis for shear strength of rock discontinuities

The theoretical basis for evaluating shear strength in rock joints is presented and used to derive an equation that governs the relationship between tangential and normal stress on the joint during situations of slippage between the joint faces. The dependent variables include geometric dilatancy, the instantaneous friction angle, and a parameter that considers joint surface roughness. The effect roughness is studied, and the aforementioned formula is used to analyse joints under different conditions. A mathematical expression is deduced that explains Barton's value for the joint roughness coefficient (JRC) according to the roughness geometry. In particular, when the Hoek and Brown failure criterion is used for a rock in the contact with the surface roughness plane, it is possible to determine the shear strength of the joint as a function of the relationship between the uniaxial compressive strength of the wall with the normal stress acting on the wall. Finally, theoretical results obtained for the geometry of a three-dimensional joint are compared with those of the Barton's formulation

The lattice solid model to simulate the physics of rocks and earthquakes: Incorporation of friction

The particle-based lattice solid model developed to study the physics of rocks and the nonlinear dynamics of earthquakes is refined by incorporating intrinsic friction between particles. The model provides a means for studying the causes of seismic wave attenuation, as well as frictional heat generation, fault zone evolution, and localisation phenomena. A modified velocity-Verlat scheme that allows friction to be precisely modelled is developed. This is a difficult computational problem given that a discontinuity must be accurately simulated by the numerical approach (i.e., the transition from static to dynamical frictional behaviour). This is achieved using a half time step integration scheme. At each half time step, a nonlinear system is solved to compute the static frictional forces and states of touching particle-pairs. Improved efficiency is achieved by adaptively adjusting the time step increment, depending on the particle velocities in the system. The total energy is calculated and verified to remain constant to a high precision during simulations. Numerical experiments show that the model can be applied to the study of earthquake dynamics, the stick-slip instability, heat generation, and fault zone evolution. Such experiments may lead to a conclusive resolution of the heat flow paradox and improved understanding of earthquake precursory phenomena and dynamics. (C) 1999 Academic Press.

The mechanical strength of phosphates under friction-induced cross-linking

Purpose: In the present study, we consider mechanical properties of phosphate glasses under high temperatureinduced and under friction-induced cross-linking, which enhance the modulus of elasticity. Design/methodology/approach: Two nanomechanical properties are evaluated, the first parameter is the modulus of elasticity (E) (or Young's modulus) and the second parameter is the hardness (H). Zinc meta-, pyro - and orthophosphates were recognized as amorphous-colloidal nanoparticles were synthesized under laboratory conditions and showed antiwear properties in engine oil. Findings: Young's modulus of the phosphate glasses formed under high temperature was in the 60-89 GPa range. For phosphate tribofilm formed under friction hardness and the Young's modulus were in the range of 2-10 GPa and 40-215 GPa, respectively. The degree of cross-linking during friction is provided by internal pressure of about 600 MPa and temperature close to 1000°C enhancing mechanical properties by factor of 3 (see Fig 1). Research limitations/implications: The addition of iron or aluminum ions to phosphate glasses under high temperature - and friction-induced amorphization of zinc metaphosphate and pyrophosphate tends to provide more cross-linking and mechanically stronger structures. Iron and aluminum (FeO4 or AlO4 units), incorporated into phosphate structure as network formers, contribute to the anion network bonding by converting the P=O bonds into bridging oxygen. Future work should consider on development of new of materials prepared by solgel processes, eg., zinc (II)-silicic acid. Originality/value: This paper analyses the friction pressure-induced and temperature–induced the two factors lead phosphate tribofilm glasses to chemically advanced glass structures, which may enhance the wear inhibition. Adding the coordinating ions alters the pressure at which cross-linking occurs and increases the antiwear properties of the surface material significantly.